Answer
Both sides of the equation in Newton's formula are equal, which verifies the accuracy of the information given in the question.
Work Step by Step
$a = 7$
$b = 7\sqrt{3}$
$c = 14$
$A = 30^{\circ}$
$B = 60^{\circ}$
$C = 90^{\circ}$
We can find the value of the left side of Newton's formula:
$\frac{a+b}{c} = \frac{7+7\sqrt{3}}{14} = 1.366$
We can find the value of the right side of Newton's formula:
$\frac{cos~\frac{1}{2}(A-B)}{sin~\frac{1}{2}C} = \frac{cos~\frac{1}{2}(30^{\circ}-60^{\circ})}{sin~\frac{1}{2}90^{\circ}}$
$\frac{cos~\frac{1}{2}(A-B)}{sin~\frac{1}{2}C} = \frac{cos~\frac{1}{2}(-30^{\circ})}{sin~45^{\circ}}$
$\frac{cos~\frac{1}{2}(A-B)}{sin~\frac{1}{2}C} = \frac{cos~(-15^{\circ})}{sin~45^{\circ}}$
$\frac{cos~\frac{1}{2}(A-B)}{sin~\frac{1}{2}C} = 1.366$
Both sides of the equation in Newton's formula are equal, which verifies the accuracy of the information given in the question.
